PharmPK Discussion - Vc lower than plasma volume

On 26 Jan 2000 at 23:53:51, "Stuart Friedrich" (SFriedrich.-at-.genetics.com) sent the message

Dear all,

I have a question regarding volume of distribution that I have beenunable to solve. I have analyzed numerous sets of serumconcentration-time data for three different monoclonal antibodyproducts in three different primate species (including humans) andfound a central volume of distribution that is lower than plasmavolume. Two of the antibodies are targeted against cell surfacereceptors and the other is against a cytokine. The analysis used todetermine central volume of distribution is model independent andtherefore does not involve extrapolation errors. A Vc markedly lowerthan plasma volume can be calculated by taking the dose and dividingby the concentration measured after an IV bolus dose. The timepointsused for the calculation can be up to several hours after the dose,so an argument based on incomplete mixing does not hold. The Vccalculated this way can range from 25 to 65% of plasma volume,assuming a plasma volume of 40 - 45 mL/kg. The data within aparticular study is tight with a CV of less than 10%. Calculating aVc that is higher than plasma volume can always be explained by sometype of binding phenomena or rapid extravascular distribution, but Icannot think of a physiological reason that would explain a Vc thatis markedly lower than plasma volume. The assays used to measure theantibodies and the doses administered are validated, so there doesnot seem to be a measurement error. I was wondering if anyone has anexplanation for this observation, and/or has seen this for othermonoclonal antibody products.

However, methods for calculating Vd, whether model dependent ormodel independent, assume a linear system. So that equations such asthe following are based on linear pharmacokinetics where the system isdescribed by linear differential equations.

ii) Vd= [Dose]/[K*AUC] equation 2

iii) Vss= D[AUMC]/[AUC]2 equation 3

A system in which the drug elmination is nonlinear due to the effectsof protein binding, equations 2 and 3 would be inaccurate.

One could reason that equation 1 accurately describes the Vd of themonoclonal antibody, but due to nonlinearities in protein binding, equations2 and 3 might not accurately predict the Vd.

Factors affecting plasma protein binding of drugs have beenfound to also affect the T1/2:

iv) High extraction drugs:

T1/2 = [Vb+ Vt(Fb/Ft)](.693)/Q equation 4

v) Low extraction drugs:

T1/2 = [Vb + Vt(Fb/Ft)](.693)/FbCli equation 5

Both of these equations are obtained from:

T1/2= (.693)(Vd/Cl) Cl= Q or Cli Vd= (Vb +Vt(Fb/Ft)]

Monoclonal antibodies should be highly protein bound and could besubject to the nonlineariries described by equations 4 and 5. This couldrender even model independent methods of determining Vd inaccurate, sincethe uderlying assumptions require linear pharmacokinetic systems.

Perhaps a more sophisticated method of calculating Vd would beappropriate.

I don't know the detail of your calculation. If you use Vc=DOSEiv/Co,Co has to be the concentration at time zero that could be calculatedfrom extrapolation of the first several time points. The first one ortwo points might affect regression a lot. If injection of dose wasnot an ideal bolus dose, Co might be under-estimated and Vc would beover-estimated. It might be better to calculate apparent volume ofdistribution (Vss=CL*MRT=DOSEiv*AUMC/AUC2). It is only for yourconsideration. Good luck.

Having administered monoclonal antibody or fragments to some well over 2,000human subjects/patients and often observed the same, It was reported in theliterature (Webster et al, J. Nucl Med, 1992)

However, in thinking about it, I believe it is when we drew blood samplesfrom the same site as we injected the MAb that we saw it. and it wassignificant enough to influence the means. The other thing to be aware of,is if you are dealing with patients with GI cancer, they have significantbleeding and their plasma compartment may indeed be larger. Remember also,there is a great amount of "non-specific" MAb binding.

Model independent or not, volumes are proportionality constants thatfunction to balance the equation where you measure a concentration in massper volume from the subject but you administered mass. The Volume ofdistribution term is necessary to put a volume term on both sides of theequation. Veng-Pederson is fond of referring to "theoreticalpharmacokinetic space" in model independent work.

So anyway, since you calculated dose/concentration and you are sure of yourdose, then it has to be the concentration term is "too high" for somereason. That reason could be the MAb still in the vessel and not mixed inthe circulation well.

Having looked at many radiolabeled MAb Planar and SPECT scans after bolusadministration, I can see and report with some certainty that the MAbradioactivity does remain in the vessel where it is administered for sometime. We always, (NOW) use a contralateral limb for sampling.

On 1 Feb 2000 at 21:39:46, ml11439.-a-.goodnet.com (Michael J. Leibold) sent the message

Art,

The textbook equations I was referring to show that changes inprotein binding can change the Vd, which in turn can change theT1/2 and Ke:

iv) High extraction drugs:

T1/2 = [Vb+ Vt(Fb/Ft)](.693)/Q equation 4

v) Low extraction drugs:

T1/2 = [Vb + Vt(Fb/Ft)](.693)/FbCli equation 5

Both of these equations are obtained from:

T1/2= (.693)(Vd/Cl) Cl= Q or Cli Vd= (Vb +Vt(Fb/Ft)]

Equation 4 and 5 predict a decrease in Vd with a decrease in thefree fraction (Fb) in the blood volume, which in turn would cause adecrease in T1/2. Similarly, an increase in free fraction in theextravascular space (Ft) would cause a decrease in Vd, and a decreasein T1/2.

The corresponding increase in Ke during the elimination of thedrug from the body would make the linear assumptions of the followingequations invalid, since the assumptions include linear "constants"of elimination:

ii) Vd= [Dose]/[K*AUC] equation 2

iii) Vss= D[AUMC]/[AUC]2 equation 3

Extrapolating plasma concentrations to time zero for a plasmaconcentration curve which is not log-linear, could result in variouscalculated Vd's depending on what portion of the curve is used, andwhether the Ke is decreasing of increasing as a result of protein binding.

In a simplified sense, if the Ke is estimated in an increasing phase,then equation 2 would predict an decreased Vd.

I checked the lab times and the dosing times. Also checkedthe nursing notes for documentation of med administration, rate ofadministration and total volume used for infusion.

Everything is in order. Point to make... All of the equations in the world will not predict whatindividual patients do on any given day. Equations were based onhealthy males 19 to 25 yrs old, not 31 week old preemies with heartproblems leading to poor renal perfusion.

I have been following levels and doses of various drugs forseveral years in a busy PICU. Kids and sick people in general, donot follow the rules.

If any of you can give me the set of equations to treat thiskind of patient, I will send you six of my best white camels anddance at your next wedding.

Please don't interpret this post as a knock on what you guysdo. We need the work. But please temper any pronouncement with agrain of salt to consider the clinical picture of the target audience.

>All of the equations in the world will not predict what individual>patients do on any given day.

How true!.

>Equations were based on healthy males 19 to 25 yrs old, not 31 week old>preemies with heart problems leading to poor renal perfusion.

And this is specially relevant in special populations (e.g., infants), or inacute diseases (e.g., cancer), where each patient presents a unique set ofpathophysiological characteristics.

In all those patients, one must measure, and then attempt to individuallyoptimized dosages.

There is one additional critical issue. What does one measure? When bloodlevels of drugs are the rate determining step, then it is possible to useblood measurements. But when the critical site to measure is a tissue (e.g.,a tumor), that is what one must measure. But repetitive and sequentialmeasurements in tissues and organs must be done noninvasively. Not only forethical considerations, but also because only those measurements that do notperturb the system being studied will have any meaning.

The pharmacy staff at our "geriatric" hospital has been using Datakineticsfor vancomycin and gentamicin dosing for ~10 years. The equations usedin the Datakinetics program are Sawchuk-Zaske like equations. Steady-stateis assumed for each calculation and the peak and trough are inserted intothe equations as if the trough was actually taken after the reported peak[a steady-state assumption].

NOTE: STEADY-STATE IN YOUR PATIENT WOULD AROUND THE 5TH DOSE[ie 24 HOURS]. LEVELS DRAWN BEFORE THIS WOULD NOT BE AT STEADY-STATE.

The mathematical model assumed is a one compartment intermittentinfusion, and the equations are as follows:

The calculated regimen is a 20mg/kg/hr one hour infusion every 12 hoursfor a predicted steady-state peak of 30.3 ug/ml and trough of 7.9 u/ml. Theliterature suggests the following regimens: i) 10mg/kg every 6 hours ii) 22.5mg/kg every 12 hours iii) 10mg/kg every 12 hours

The calculated pharmacokinetic values do not deviate significantlyfrom the literature values, and the calculated regimen agrees with one ofthe literature suggested regimens. Changing renal/cadiovascular functionrequires frequent monitoring of vancomycin levels for further dosageadjustments.

Please do not misconstrue my remarks in the earlier post. On manyoccasions I use standard equations to predict levels and guidetherapy. The work of the pharmacokineticist is invaluable here. Theyset the baseline against which we measure/compare those patients whofall outside the standard parameters. (I know what the drug shoulddo, but this is what it is doing.... Scratch head, look puzzled.)

The problems arise in treating specific diseases andpathophysiological conditions that alter the regular physiology inways we have yet to determine. The most common confounding statesbeing ARDS, MOSD, Sepsis, Multiple Trauma, Sickle Cell and many typesof cancers.

These are the train wrecks that turn up on our doorstep whereclinical knowledge/experience coupled with a firm grasp of harderscience comes into play.

If it were easy, I would be selling popcorn in St. Martin.Keep up the good work ladies and gentlemen. We need you, the patients need us.

On 16 Feb 2000 at 21:56:56, Roger Jelliffe (jelliffe.-a-.usc.edu) sent the message

Dear Robert:

You are absolutely right. All population models are like yesterday'snewspaper. Even if your patient was an adult, the use of population modelsalone is usually NOT enough, because of the diversity in the population.But they are all one has. Any initial dosage regimen, based on anypopulation model, NEEDS to be followed up by measuring levels and making anindividualized model of how that drug is behaving in that particularpatient. That is the whole purpose of getting feedback. That is what Bayes'theorem is all about. The set of equations you need is simply obtained byfitting the model to your patient's data, and using that patient'sindividualized model to compute the regimen to achieve the desired targetgoal(s). Most software, including our own USC*PACK Bayesian software, isdesigned to do just this. Put in the dosage regimen. Put in the levels. Fitthe model. See the plot. Compare the behavior of the plot with the clinicalbehavior of the patient. That is the only way I know to really evaluate thepatient's clinical sensitivity to a drug. Then consider your target goals,and find the best combination of dose and dose interval to best hit yourtarget goals. Also, what does your patient weigh?

After this is over, you will get experience with patients such as thisone, and you then can store your experience by making a population model ofthe patients you have studied, in exactly the clinical situations which arerelevant. This will help you get a better Bayesian prior for use indesigning the initial regimen to hit your target goals. Yo might alsoconsider looking at our web site (see below) for more info, especially inour technical reports and other publications.